>>>>Just because a regulation doesn't specifically forbid a certain action doesn't mean it allows it.
Ummm, actually, yes it does. That's one of the principles of our legal system: In order for something to be against the law, there must be a law (statute, regulation, administrative code, whatever) making it against the law.
If not, then we would be subject to following unwritten laws, and if the laws are unwritten, well, how are we to know what they are?
>>>>>For example, 61.51 doesn't say anything about recent experience requirements.
Right ..... so???? 61.51 regulates what you may write in your logbook, not what planes you may fly and when.
>>>>>>>However, you still can't act as PIC unless you are current.
yes, I think we all agree that's true, and it is because 61.57 says you may not act as pilot in command unless you meet certain currency requirements. That doesn't have anything to do with 61.51.